Optimal estimators for distributed-parameter systems with time-averaged pointwise measurements

The optimal linear estimators for distributed-parameter systems are derived in the case of pointwise observations that are time-averaged during the sampling interval. The filter structure derived is compared with that for the discrete-time observation case, and the finite-dimensional approximation of the results is presented.     

Optimal linear estimators for systems with random measurement delays

This paper is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with random measurement delays. A new model that describes the random delays is constructed where possible the largest delay is bounded. Based on this new model, the optimal linear estimators including filter, predictor and smoother are developed via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. The steady-state estimators are also investigated. A sufficient condition for the convergence of the optimal linear estimators is given. A simulation example shows the effectiveness of the proposed algorithms.     

Optimal linear estimators for systems with multiple random measurement delays and packet dropouts

This article is concerned with the optimal linear estimation problem for linear discrete-time stochastic systems with possible multiple random measurement delays and packet dropouts, where the largest random delay is limited within a known bound and packet dropouts can be infinite. A new model is constructed to describe the phenomena of multiple random delays and packet dropouts by employing some random variables of Bernoulli distribution. By state augmentation, the system with random delays and packet dropouts is transferred to a system with random parameters. Based on the new model, the least mean square optimal linear estimators including filter, predictor and smoother are easily obtained via an innovation analysis approach. The estimators are recursively computed in terms of the solutions of a Riccati difference equation and a Lyapunov difference equation. A sufficient condition for the existence of the steady-state estimators is given. An example shows the effectiveness of the proposed algorithms.     

Optimal minimal order N-State estimators for linear stochastic systems

This paper presents the general solution to the problem of designing minimal order estimators to optimally estimate the state vector x_k of a linear discrete-time stochastic system with time invariant dynamics. The estimators differ depending on the number N of stages over which the estimates $\text{X}\text{?}{}_{\mathrm{1N\; +\; 1}}\text{, …,}\text{X}\text{?}{}_{\mathrm{1N\; +\; N}}$ are to be recursively determined for l= 0, 1, 2, . … The optimal steady state estimator is obtained in the limit as N goes to infinity.     

Optimal measurement trajectories for distributed parameter systems

The paper deals with the optimal sensor location problem associated with minimax filtering for linear distributed parameter systems under the moving sensors. The problem of optimal choice of a measurement trajectory is treated here as an H^∞-optimal control one under phase constraints with the objective to minimize a given ‘weak’ performance index under ‘worst’ possible disturbances. Existence of a solution to such a problem is established for the case of quadratic constraints on the disturbances and necessary conditions for optimally are derived on the basis of constructing a sequence of suboptimal solutions associated, in turn, with a sequence of finite-dimensional maximum principles.     

具有有限连续丢包网络控制系统的最优线性估值器

本文研究了观测数据和控制输入数据传输具有有限连续丢包的线性离散随机系统的最优估计问题.利用两个满足Bernoulli分布的随机变量来分别描述从传感器到估值器和从控制器到执行器之间的数据丢包现象.通过引入两组新的变量,将原系统转化为一个带有随机参数的系统.利用射影理论,提出了线性最小方差最优线性估值器,包括滤波器、预报器和平滑器.最后研究了稳态线性估值器,并给出了稳态存在的一个充分条件.仿真例子验证了算法的有效性.     

Optimal convex error estimators for classification

A cross-validation error estimator is obtained by repeatedly leaving out some data points, deriving classifiers on the remaining points, computing errors for these classifiers on the left-out points, and then averaging these errors. The 0.632 bootstrap estimator is obtained by averaging the errors of classifiers designed from points drawn with replacement and then taking a convex combination of this “zero bootstrap” error with the resubstitution error for the designed classifier. This gives a convex combination of the low-biased resubstitution and the high-biased zero bootstrap. Another convex error estimator suggested in the literature is the unweighted average of resubstitution and cross-validation. This paper treats the following question: Given a feature-label distribution and classification rule, what is the optimal convex combination of two error estimators, i.e. what are the optimal weights for the convex combination. This problem is considered by finding the weights to minimize the MSE of a convex estimator. It also considers optimality under the constraint that the resulting estimator be unbiased. Owing to the large amount of results coming from the various feature-label models and error estimators, a portion of the results are presented herein and the main body of results appears on a companion website. In the tabulated results, each table treats the classification rules considered for the model, various Bayes errors, and various sample sizes. Each table includes the optimal weights, mean errors and standard deviations for the relevant error measures, and the MSE and MAE for the optimal convex estimator. Many observations can be made by considering the full set of experiments. Some general trends are outlined in the paper. The general conclusion is that optimizing the weights of a convex estimator can provide substantial improvement, depending on the classification rule, data model, sample size and component estimators. Optimal convex bootstrap estimators are applied to feature-set ranking to illustrate their potential advantage over non-optimized convex estimators.     

Distributed estimators for nonlinear systems

A nonlinear distributed estimation problem is solved by using reduced-order local models. Using local models with lower dimensions than the observed process model will lessen the local processors' complexities or computational loads. Fusion algorithms that combine local densities to construct the centralized density of a nonlinear random process are presented. The local densities are generated at each measurement time and communicated to a coordinator. The models used to produce these densities are reduced-order valid models. The validity of the local models guarantees that the coordinator reconstructs exactly the centralized density function     

Optimal quadrature formula nonlinear estimators

This paper presents a method for the realization of nonlinear estimators based on an optimal quadrature approximation. The optimal quadrature formula is obtained by solving a set of nonlinear algebraic equations induced from a monospline subject to a set of interpolatory conditions. All the weights of the optimal quadrature formulas derived from monosplines which do not involve the derivatives of the integrand at the end points are positive. This guarantees the positiveness of the quantized density functions in numerical approximation of Bayesian recursive computations. The numerical errors associated with the optimal quadrature approximation to Bayesian recursive computations are discussed. Finally methods of quantizing and updating the prediction and filtering densities are derived.     

有界随机测量时滞的网络控制系统的最优估计

在假设测量没有丢包的情况下, 研究了带有随机测量时滞的网络控制系统的最优估计问题. 利用已知的时 滞分布概率, 建立新的模型来描述随机时滞测量. 进一步将带有时滞的测量等价成每个通道是单时滞的多通道测 量, 从而利用新息重组方法, 通过求解黎卡提方程求解最优估计器. 最后给出仿真实例验证了该算法的有效性.     

Optimal and suboptimal separate-bias Kalman estimators for astochastic bias

Addresses two issues concerning the separate-bias Kalman estimator. The first of these issues deals with the derivation of the optimal estimator for the general case in which the bias vector is stochastic in nature, and the second issue deals with defining a suitable suboptimal realization of the generalized estimator     

带乘性噪声和延时观测广义系统的多步最优预测器

本文研究了状态空间描述的离散广义系统最优预测器的设计问题,该系统带有即时和延时观测,所有观测中带有乘性噪声.论文在两个基本假设条件下采用标准的奇异值分解方法给出了受限等价时滞系统,对于此类系统没有采用状态增广方法,而是采用新息重组分析理论给出了多步预测器.因为延时观测的存在,所给出的多步预测器包含了两套递推的广义系统黎卡提方程.本文给出了一个数学算例验证了所提方法的正确性和有效性,并给出了四幅图片,根据算例可以看出一般情况下预测的步数越少,预测的结果越好.本文方法可以进一步来研究更复杂的一些问题,如延时广义系统的H_∞滤波和控制问题.     

Optimal control of discrete-time uncertain systems with imperfect measurement

We consider a discrete-time optimal control problem in the presence of uncertainties in the dynamics and in the measurement. An optimal (in min-max sense) output-feedback controller is derived from a discrete Bellman equation. We propose a formulation of the last equation in the estimation space, which allows approximation by a reduced-order equation corresponding to a prescribed collection of estimation sets. The approach is illustrated up to numerical experiments by a pursuit-evasion game on the plane, with incomplete information of the current state of the evader.     

Robust centralized and weighted measurement fusion Kalman estimators for uncertain multisensor systems with linearly correlated white noises

This paper addresses the design of robust centralized fusion (CF) and weighted measurement fusion (WMF) Kalman estimators for a class of uncertain multisensor systems with linearly correlated white noises. The uncertainties of the systems include multiplicative noises, missing measurements, and uncertain noise variances. By introducing the fictitious noises, the considered system is converted into one with only uncertain noise variances. According to the minimax robust estimation principle, based on the worst-case system with the conservative upper bounds of uncertain noise variances, the robust CF and WMF time-varying Kalman estimators (predictor, filter, and smoother) are presented in a unified framework. Applying the Lyapunov equation approach, their robustness is proved in the sense that their actual estimation error variances are guaranteed to have the corresponding minimal upper bounds for all admissible uncertainties. Using the information filter, their equivalence is proved. Their accuracy relations are proved. The computational complexities of their algorithms are analyzed and compared. Compared with CF algorithm, the WMF algorithm can significantly reduce the computational burden when the number of sensors is larger. A robust weighted least squares (WLS) measurement fusion filter is also presented only based on the measurement equation, and it is proved that the robust accuracy of the robust CF or WMF Kalman filter is higher than that of robust WLS filter. The corresponding robust fused steady-state estimators are also presented, and the convergence in a realization between the time-varying and steady-state robust fused estimators is proved by the dynamic error system analysis (DESA) method. A simulation example shows the effectiveness and correctness of the proposed results.     

Optimal placement of phasor measurement systems for enhancing on-line protection and control of large-scale power systems

Microprocessor-based real-time phasor measurements, i.e. measurement of fundamental frequency, positive sequence, complex three phase voltages and currents, for enhancing on-line protection and control of interconnected electric power systems are described. The proposed research demonstrates that real-time monitoring of key system states, in the bulk power transfer problem, can be identified. It also provides the means for determining which states are the key states for that problem, and that phasor measurements can be used to improve the protection and/or control of the system. The procedure is applied to a realistic system, where such a control problem exists in practice, for confirmation of the developed technique.     

Large-deviation inequalities for parameter estimators in stochastic systems

Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 95–112, March–April, 1994.     

Reduced order state estimators for discrete-time stochastic systems

A reduced order, least squares, state estimator is developed for linear discrete-time systems having both input disturbance noise and output measurement noise with no output being free of measurement noise. The order reduction is achieved by using a Luenberger observer in connection with some of the system outputs and a Kalman filter to estimate the state of the Luenberger observer. The order of the resulting state estimator is reduced from the order of the usual Kalman filter system state estimator by the number of system outputs selected for use as inputs to the Luenberger Observer. The manner in which the noise associated with the selected system outputs affects the state estimation error covariance provides considerable insight into the compromise being attempted.     

A note on finite-dimensional estimators for infinite-dimensional systems

In this note we prove two theorems regarding finite-dimensional estimators for infinite-dimensional systems. The first concerns the finite dimensionality of the model and the second concerns the finite dimensionality of the observation space. Our analysis applies to very general systems, but appears to be most useful for the estimation of static systems from point sensing.     

Discrete state estimators for systems on a lattice

We address the problem of estimating discrete variables in a class of deterministic transition systems in which the continuous variables are available for measurement. We propose a novel approach to the estimation of discrete variables using lattice theory that overcomes some of the severe complexity issues encountered in previous work. The methodology proposed for the estimation of discrete variables is general as it is applicable to any observable system. Extensions generalize the approach to nondeterministic transition systems. The proposed estimator is finally constructed for a multi-robot system involving two teams competing against each other.     

时变系统的统一和通用的最优噪声估值器

对于带相邻及同一时刻相关噪声的时变系统,基于Kalman滤波理论提出了统一和通用的最优噪声估值器,包括观测噪声估值器和输入噪声估值器,提出了统一和通用的固定点和固定区间的最优噪声平滑器,它们为解决状态和信号估计问题提供了新的工具.一个仿真算例说明了其有效性.